Having lived here 9 years now, I can honestly say there are no really bad times of year weather-wise in Cozumel! That's the great thing about our tropical setting...it's never bad as compared to other places further north! But, understanding what you're getting at with regard to dive conditions etc. here are a few guidelines to determine if you would be happy/comfortable diving during these time frames:
March-June:SPRING/SUMMER seas are usually flat, skies sunny...alot of "no cloud" days, water temp 78-80 and viz from 100 - 300+ depending on if we get any rains. These months riding on the boat is pleasantly warm because humidity is less and alot of sunscreen is needed.
July-Oct:RAINY SEASON seas are usually flat, skies are more cloudy and rain comes/goes throughout the day with no real rhyme or reason so it's very humid [70%+] as well as warm. Water temp will be 80-84 and 300+ viz if the rains are scattered. This is also part of our hurrican/tropical storm time....if these roll thru ~ all bets are off on water conditions obviously!! However, with that said this is also a great time to be here diving if there is no "weather"...fewer divers, fewer people in general.
Nov-Feb: WINTER Seas will be lightly choppy, most days it will be sunny with skies partly cloudy and water temps will go from 84 down to 78-80 range. Viz will be very good generally. During winter we get "nortes" that blow in from time to time and shut down diving for 2-3 days. Also, the boat rides can be chilly for sometimes there are low north winds and diving goes on.
These conditions only affect your personal comfort so you can best decide what you are willing to tolerate ~
As far as critters go...they are here no matter what the weather although you are more likely to see larger stuff during the winter months when the water is cooler...especially the spotted eagle rays!
Just become a frequent visitor and you'll see that any day diving beats being somewhere else no matter the time of year!!
Hope this helps some!!